Basic Linear Algebra

About the Book

This book is an introductory linear algebra text. The topics are covered in the traditional order: linear systems, matrix algebra, vector spaces, linear transformations, orthogonality, and the eigenvalue/eigenvector problem. The book seeks to explain and discover the important concepts of linear algebra using well-chosen examples. Proofs of many important results are done if the proof can be accomplished in a succinct, straightforward fashion. There are over 100 worked-out examples in the text as well as a complete outline of every chapter and extensive review problems which test the student’s knowledge of the material covered in each chapter. There are over 1200 exercises in the text, which were created by the author with care to include exercises which resemble problems done in the text. Definitions are well marked and theorems are stated as briefly as possible in order to enhance the ability of the student to remember the result. In a slightly novel way, the answers to the odd problems are given directly next to the problem. Applications such as heat transfer, spring/mass systems, population dynamics, and systems of differential equations are sprinkled throughout the text.

About the Author

The author has been teaching at Penn State Erie since 1984. He holds a Bachelor’s degree from Gannon University and a Master’s degree from the University of Pittsburgh. He has had several articles published in journals such as Mathematics Magazine and has taught the linear algebra course many times.